Relation Between Speed of Light & Reflected Angle (Fizeau–Foucault) I have a bachelor's in physics & its recently struck me that I do not understand, semantically, what phenomenon allows us to measure the speed of light through air in a small room with a laser and a spinning mirror. 
I understand "the how," which is to say I know that measuring the angle reflected by a beam (fired at a fixed distance) against a mirror (rotating at high angular velocity) allows us to measure the speed of that beam. What i do not understand is why this experimental method is possible, and therefore satisfactory to claim measurement of a finite speed.  
For a typical Fizeau–Foucault method setup:
If the beam is continuous & mirror perfectly flat, shouldn't light always get reflected at whatever angle is governed by normal geometry?...as a result, I would imagine a wedge of light having fixed-width, & depending only on the spatial coordinates of the mirror, not on t.
To help try and make my question clearer, I made a diagram. The red arrows are how I would expect light to be reflected off of a spinning flat mirror:

 A: Think of the beam from the rotating mirror like a beacon from a lighthouse. This beam is sent to a distant mirror. As it sweeps across the distant mirror only a small portion of the beam will be reflect directly back to the rotating mirror. 
My daughter and I actually did this experiment in our garage. I ended up adding additional mirrors which caused the returning beam to be even more precise. What I mean by precise is the return beam had a very narrow passage back to the rotating mirror. 
What I have described in this answer is how a rotating mirror and a distant mirror can create a movement of light that is measurable. I am not sure if it matches the details of fizeau’s experience, but I believe it addresses your question.
A: The rotating mirror is hit twice, on the way to and returning from another distant mirror, but at different angles, such that the return light forms an image slightly offset from the source. 
When the rotating mirror is static, the outgoing and return angle are the same and the image coincides with the source
